If your server know about your child's birthday then they will certainly bring a cake out to him. I think that when you make your reservation they ask if you are celebrating any special occasion, so you can tell them then, and they will have it on file for the special day.
When the DH and I cruised the last time, it was the DH's b-day, so I ordered the Birthday stateroom celebration for him, and I thought it was quite cute. There are people here who will tell you that it's not worth the money to them, and they bring their own decorations, but to me the $30 is worth it for it all to be in the room when you arrive!